how to make absolut value in python model

Answered

Rahadyan Bagus P

January 04, 2024 04:44

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i want to change G[i,j] into | X[i] - X[j] |

model.setObjective(grb.quicksum(Cobj[i,j]*G[i,j] for i in N for j in N if i<j))

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  Jaromił Najman

  • Gurobi Staff

  January 04, 2024 08:12 Edited

  You can use the addGenConstrAbs method to do that. You will have to formulate

  \[\begin{align*}
  z_{ij} &= X_i - X_j\\
  G_{ij} &= |z_{ij}|
  \end{align*}\]

  or in Python (pseudo code)

  # add a free auxiliary variable to the model
  z[i,j] = model.addVar(lb=-GRB.INFINITY, name="z"+str(i)+str(j))
  # add constraint z_ij = X_i - X_j
  model.addConstr(X[i] - X[j] == z[i,j], name="aux_constr_"+str(i)+str(j))
  # add constraint G_ij = |z_ij|
  model.addGenConstrAbs(G[i,j], z[i,j], "absconstr_"+str(i)+str(j))

  Note that it is necessary to introduce an auxiliary variable \(z_{ij}\) because the addGenConstrAbs method accepts only single optimization variables as input arguments. Moreover, it is necessary to define the lower bound of \(z_{ij}\) as \(-\infty\) because the default variable lower bound in Gurobi is \(0\).

  Best regards, 
  Jaromił

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